A general non-parametric technique is proposed for the analysis of a complex multimodal feature space and to delineate arbitrarily shaped clusters in it. The basic computational module of the technique is an old pattern recognition procedure: the mean shift. For discrete data, we prove the convergence of a recursive mean shift procedure to the nearest stationary point of the underlying density function and, thus, its utility in detecting the modes of the density. The relation of the mean shift procedure to the Nadaraya-Watson estimator from kernel regression and the robust M-estimators; of location is also established. Algorithms for two low-level vision tasks discontinuity-preserving smoothing and image segmentation - are described as applications. In these algorithms, the only user-set parameter is the resolution of the analysis, and either gray-level or color images are accepted as input. Extensive experimental results illustrate their excellent performance.

Mean shift: a robust approach toward feature space analysis

Bilateral filtering smooths images while preserving edges, by means of a nonlinear combination of nearby image values. The method is noniterative, local, and simple. It combines gray levels or colors based on both their geometric closeness and their photometric similarity, and prefers near values to distant values in both domain and range. In contrast with filters that operate on the three bands of a color image separately, a bilateral filter can enforce the perceptual metric underlying the CIE-Lab color space, and smooth colors and preserve edges in a way that is tuned to human perception. Also, in contrast with standard filtering, bilateral filtering produces no phantom colors along edges in color images, and reduces phantom colors where they appear in the original image.

/pdf/bilateral-filtering-for-gray-and-color-images-jnho720ytd.pdf

Bilateral filtering for gray and color images

We investigate the properties of a metric between two distributions, the Earth Mover's Distance (EMD), for content-based image retrieval. The EMD is based on the minimal cost that must be paid to transform one distribution into the other, in a precise sense, and was first proposed for certain vision problems by Peleg, Werman, and Rom. For image retrieval, we combine this idea with a representation scheme for distributions that is based on vector quantization. This combination leads to an image comparison framework that often accounts for perceptual similarity better than other previously proposed methods. The EMD is based on a solution to the transportation problem from linear optimization, for which efficient algorithms are available, and also allows naturally for partial matching. It is more robust than histogram matching techniques, in that it can operate on variable-length representations of the distributions that avoid quantization and other binning problems typical of histograms. When used to compare distributions with the same overall mass, the EMD is a true metric. In this paper we focus on applications to color and texture, and we compare the retrieval performance of the EMD with that of other distances.

/pdf/the-earth-mover-s-distance-as-a-metric-for-image-retrieval-h8u7zfx61r.pdf

The Earth Mover's Distance as a Metric for Image Retrieval

The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search/index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the \curse of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and/or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50).

/pdf/similarity-search-in-high-dimensions-via-hashing-27z92j627a.pdf

Similarity Search in High Dimensions via Hashing

We use a simple statistical analysis to impose one image's color characteristics on another. We can achieve color correction by choosing an appropriate source image and apply its characteristic to another image.

https://www.cs.tau.ac.il/~turkel/imagepapers/ColorTransfer.pdf

Color transfer between images

An encyclopedic work which collects into a ready-reference volume the concepts, methods, quantitative data and formulas on color science. Includes details of light sources, color filters, physical detectors of radiant energy, and the working concepts in color matching, discrimination, and adaptation. For the colorimetrist, research worker, physicist, physiologist and psychologist concerned with color problems in industry. Tables; diagrams; ten-page bibliography. First author is head, radiation optics section, National Research Council, Canada. Contents, abridged: Basic radiometric concepts and units. Optical filters. Physical detectors of radiant energy. Parts of the human eye: nomenclature; dimensions. Factors in the eye that control the internal stimulus. The Troland values of retinal illuminance. Light losses in the eye. Quantum fluctuations and visual stimuli. Conversion factors related to the eye. Trichromatic generalization. The CIE colorimetric system. Complementary colors. Object colors, object. color solid, optimal colors. Counting metameric object colors. Degree of metamerism. Propagation of spectrophotometric errors. The photometric principle. Preamble. Factors modifying matching. Chromatic adaptation. Lightness scales. Combined lightness and chromaticness scales. Discrimination data under special conditions. Color reversal at long wavelengths: Brindley isochromes. Abney and Bezold-Brucke effects. Dark adaptation and absolute thresholds. Uniform equivalent fields (equivalent background luminance). Visual response curves: their comparison with the spectral properties of pigments. References. Author index. Subject index. -- AATA

Color Science. Concepts and Methods, Quantitative Data and Formulas

Color Science Concepts and Methods

Spectral distributions of 622 samples of daylight (skylight, and sunlight plus skylight) have been subjected to characteristic vector analysis, as composite data and in three subgroups (99 distributions measured by Budde; 249, by Condit; and 274, by Henderson and Hodgkiss). The chromaticity coordinates (x,y) computed from these distributions have been compared with direct visual determinations of chromaticity coordinates of daylight by Nayatani and Wyszecki, and by Chamberlin, Lawrence, and Belbin. It was found that the chromaticities indicated by the spectral distributions and by direct visual colorimetry cluster about the curve: y = 2.870x−3.000x2−0.275. This curve of typical daylight chromaticities falls slightly on the green side of the Planckian locus. From the mean and the first two characteristic vectors of the composite data, spectral distribution curves have been reconstituted by choice of scalar multiples of the vectors such that the chromaticity points fall on the curve of typical daylight chromaticities at places corresponding to correlated color temperatures of 4800°, 5500°, 6500°, 7500°, and 10 000°K. The representative character of these reconstituted spectral-distribution curves has been established by comparison with the measured curves from each subgroup yielding the closest approximation to the same chromaticities. The agreement so found suggests that this family of curves is more representative of the various phases of daylight between correlated color temperatures 4800° and 10 000°K than any previously derived distributions.

Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature

Three new sets of color-matching experiments have been made by three observers binocularly viewing a bipartite field (each half subtending 3°) of a three-primary colorimeter. Each set of color-matching data refers to 28 test colors scattered over the chromaticity gamut provided by the colorimeter. The luminance of each test color was 12 cd · m−2; the white surround (subtending 40°) was maintained at 6 cd · m−2. The elliptical cross sections (for Y = const) of the observed color-matching ellipsoids are compared with results previously published by MacAdam, and Brown and MacAdam. In view of the inherent experimental uncertainties of data of this kind, the new color-matching ellipses correlate well with those obtained by Brown, and Brown and MacAdam, but show significant deviations from those obtained by MacAdam’s observer P. G. Nutting, Jr. The discrepancies are puzzling. A note of caution is added with regard to the usefulness of color-matching ellipses in testing line elements. A set of color-matching ellipses can reveal only little of the visual mechanism that governs the precision of color matching and its assumed direct correlation with judging small color differences. It appears that fundamentally different line elements can reproduce almost equally well a given set of color-matching ellipses.

Gunter Wyszecki

Papers

Color Science. Concepts and Methods, Quantitative Data and Formulas

Color Science Concepts and Methods

Spectral Distribution of Typical Daylight as a Function of Correlated Color Temperature

New Color-Matching Ellipses

Proposal for a New Color-Difference Formula